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math105-s22:notes:lecture_15

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math105-s22:notes:lecture_15 [2022/03/08 00:28]
pzhou 		math105-s22:notes:lecture_15 [2022/03/09 12:37] (current)
pzhou
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 ====== Lecture 15 ====== ====== Lecture 15 ======
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 +[[https://berkeley.zoom.us/rec/share/OvE6Kwx30h9tqRwyGp3PCtUcEp97b98ahuWVfO29jmfOGLRiEiJpwEFrfAPWnC2p.RD0hzsRPKYEE009Z | video ]]
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 Last time, we considered the (long and hard) Lebesgue density theorem, which says, given any Lebesgue locally integrable function f:Rn→Rf: \R^n \to \R, then for almost all pp, the density $\delta(p,f)of of fat at pexistsandequalstothevalue exists and equals to the value f(p)$.  Last time, we considered the (long and hard) Lebesgue density theorem, which says, given any Lebesgue locally integrable function f:Rn→Rf: \R^n \to \R, then for almost all pp, the density $\delta(p,f)of of fat at pexistsandequalstothevalue exists and equals to the value f(p)$. 
  
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 Since ϵ\epsilon is arbitrary, we do get H(a)=H(b)H(a)=H(b).  Since ϵ\epsilon is arbitrary, we do get H(a)=H(b)H(a)=H(b). 
  
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 +I will leave Pugh section 10 for presentation project. 
math105-s22/notes/lecture_15.1646728138.txt.gz · Last modified: 2022/03/08 00:28 by pzhou

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